Federal Reserve Bank of Dallas Globalizaion and Moneary Policy Insiue Working Paper No. 37 hp://www.dallasfed.org/asses/documens/insiue/wpapers/05/037.pdf Financial Fricions and Policy Cooperaion: A Case wih Monopolisic Banking and Saggered Loan Conracs * Ippei Fujiwara Keio Universiy and Ausralian Naional Universiy Yuki Teranishi Keio Universiy April 05 Absrac Do financial fricions call for policy cooperaion? This paper invesigaes he implicaions of simple financial fricions, monopolisic banking ogeher wih saggered loan conracs, for moneary policy in open economies in he linear quadraic (LQ) framework. Welfare analysis shows ha policy cooperaion improves social welfare in he presence of such financial fricions. There also exis long-run gains from cooperaion in addiion o hese by joinly sabilizing inefficien flucuaions over he business cycle, ha are usually found in models wih price rigidiies. The Ramsey opimal seady saes differ beween cooperaion and noncooperaion. Such gains from cooperaion arise irrespecive of he exisence of inernaional lending or borrowing. JEL codes: E50, F4 * Ippei Fujiwara, Faculy of Economics, Keio Universiy, -5-45 Mia, Minao-ku, Tokyo 08-8345 Japan. ippei.fujiwara@anu.edu.au. Yuki Teranishi, Faculy of Business and Commerce, Keio Universiy, -5-45 Mia, Minao-ku, Tokyo 08-8345 Japan. yukiera@fbc.keio.ac.jp. Formerly circulaed as Financial Sabiliy in Open Economies. The auhors hank he edior Giancarlo Corsei and wo anonymous referees for useful commens. We have also benefied from discussions wih Kosuke Aoki, Pierpaolo Benigno, Marin Bodensein, Larry Chrisiano, Richard Dennis, Bianca De Paoli, Mary Eichenbaum, Takeo Hoshi, Gunes Kamber, Jinill Kim, Federico Mandelman, Tomoyuki Nakajima, Sefan Niemann, Maury Obsfeld, Bruce Preson, Lars Svensson, Cedric Tille, Mike Woodford, and seminar and conference paricipans a he Universiy of Bonn, Hiosubashi Universiy, FRB Alana, Bank of Korea, Universiy of Zurich, Vicoria Universiy of Wellingon, Reserve Bank of New Zealand, Kyoo Universiy and Naional Universiy of Singapore. Fujiwara graefully acknowledges financial suppor from he Muraa Science Foundaion. The views in his paper are hose of he auhors and do no necessarily reflec he views of he Federal Reserve Bank of Dallas or he Federal Reserve Sysem.
Inroducion The recen global nancial crisis has renewed ineres in he poenial of policy cooperaion. In order for he global economy o recover, he need for policy cooperaion is now a opic of discussion for leaders in major policy insiuions. Academic sudies, however, do no usually emphasize he imporance of cooperaion in sabilizaion policies. Wha causes hese divergen views on policy prescripions during he global nancial crisis? Perri and Quadrini (0) emphasize he imporance of nancial fricions in explaining he unprecedened degree of business cycle synchronizaion across di eren counries during he recen global nancial crisis. In his paper, we ackle his problem by invesigaing he implicaions of simple nancial marke imperfecions on moneary policy in open economies. For his purpose, we exend he sandard new open economy macroeconomics (NOEM) model a la Clarida, Gali, and Gerler (00) or Benigno and Benigno (003, 006), o incorporae an imperfecly compeiive banking secor as examined in Kobayashi (008), Teranishi (05), Mandelman (00, 0), and Fujiwara and Teranishi (0). The banking secor of our model has hree feaures: a cos channel, monopoly power by banks over loan rae seings, and saggered loan conracs. Gerali, Neri, Sessa, and Signorei (00) esimae a similar model o ours, where monopolisic banking and sicky loan raes are incorporaed in a prooypical dynamic sochasic general equilibrium (DSGE) model, in order o quanify he conribuion of shocks originaing from nancial fricions o he slowdown during he recen global nancial crisis. Firms need o borrow working capial from privae banks in advance o nance wage Dr. John Lipsky, Acing Managing Direcor of he IMF, saed on June 0, A second success is he remarkable increase in global policy cooperaion ha has aken place in he wake of he 008-09 global nancial crisis. When he world las faced such grave danger during he Grea Depression counries aced in heir own, perceived self-ineres wih beggar-hy-neighbor policies ha in fac deepened he downurn. This ime, counries aced ogeher o ackle he crisis. Corsei, Dedola, and Leduc (00) conclude ha, [i]n welfare erms, he gains from cooperaion are close o zero. Indeed, he lieraure has presened numerical assessmens of he benchmark model under he complee markes ha do no generae appreciable quaniaive welfare gains from coordinaing policies, relaive o opimal sabilizaion pursued by independen policy makers (engaging in sraegic manipulaion of erms of rade).
bills. Barh and Ramey (00) and Ravenna and Walsh (006) empirically demonsrae he imporance of his cos channel in moneary policy ransmission in he US. Each bank is assumed o be in a long-erm relaionship wih each inermediae-goods producing rm. Thus, banks have monopoly power over loan rae seings. Gropp and Kashyap (00), van Leuvenseijn, Sorensen, Bikker, and van Rixel (03) and Mandelman (00, 0) explore he imporance of bank compeiions on loan rae seings. Finally, dynamic fricions in he nancial marke are capured by saggered loan conracs, ha follow he Calvo (983) - Yun (996) framework. Sickiness in loan rae conracs is repored by many sudies, as Slovin and Sushka (983) and Berger and Udell (99) for he U.S., Sorensen and Werner (006) and Gambacora (008) for he Euro area, and he Bank of Japan s Financial Sysem Repors for he Japanese economy. 3 Their explanaions rely on credi raioning during recession. There are, however, oher aspecs relaing o sickiness in loan raes. For example, he Bank of Japan s Financial Sysem Repors show ha he duraion of xed loan conracs ends o be very long. Also, Graham and Wrigh (007) repor ha a signi can proporion of ineres rae paymens in some European counries are a a xed rae. Furhermore, hey noe ha []he associaed deb conracs are almos always wrien in nominal erms, have quie signi can associaed ransacions coss and as a consequence are renegoiaed relaively infrequenly. 4 We hen use a NOEM model wih such nancial fricions o analyze he opimal 3 For he US, using micro level daa, Slovin and Sushka (983) and Berger and Udell (99) show ha i akes wo or more quarers for he privae banks o adjus loan ineres raes. For he Euro area, Sorensen and Werner (006) esimae he incompleeness in he pass-hrough from he policy ineres rae o loan ineres raes in an error correcion model using macro daa. They furher show ha he degree of he incomplee pass-hrough signi canly di ers among counries. Gambacora (008) conducs similar analysis for Germany and shows he exisence of sicky adjusmen in loan ineres raes. For Japan, according o Bank of Japan s Financial Sysem Repors published in March 007 and 008, he major ciy banks need ve quarers and he local banks seven quarers o adjus loan ineres raes. 4 Several sudies provide empirical evidences behind hese infrequen negoiaions, for example, Hannan and Berger (99) for menu coss, Berger and Udell (99) for implici conracs and Calem, Gordy, and Meser (006) for swiching coss. 3
moneary policy under boh cooperaion and noncooperaion. In order o undersand how simple nancial fricions as explained above may aler gains from cooperaion, a linear quadraic (LQ) approach is employed. The second order approximaed welfare meric following Benigno and Woodford (005) and Benigno and Benigno (006) is also derived. Saggered loan conracs under monopolisic compeiion in he banking secor creae dispersion in loan raes when a shock his he economy. Since labor supply is ighly linked o loan raes due o he working capial loan, his resuls in ine cien allocaions in labor among ex pos symmeric rms. Consequenly, similarly o he case wih price rigidiies, dispersion in loan raes works as if i were a negaive echnology shock. The role of he cenral bank is o reduce welfare loss semming from such dispersion in loan raes and he working capial loan. Welfare analysis shows ha here are boh long-run and shor-run gains in cooperaion. Seady sae welfare becomes higher under cooperaion. Under noncooperaion, each cenral bank has long-erm incenives o raise loan ineres raes. This is because high ineres raes reduce labor supply via he cos channel. This resul is similar o he one obained in Cooley and Quadrini (003). Over he business cycle, here also exis gains from cooperaion when he global economy is subjec o markup shocks. This is because he erms of rade exernaliy, where each counry aemps o manipulae he erms of rade in is favor, is no inernalized under noncooperaion. 5 These resuls hold regardless of he exisence of inernaional lending or borrowing. Unless here is fricion in inernaional nancial ransacions, neiher inernaional lending nor borrowing makes any di erence o he case in which only domesic nancial ransacions are allowed. The res of he paper is srucured as follows. Previous sudies wih similar banking secors o ours in a dynamic general equilibrium framework are summarized in Secion 5 The mechanism behind his resul is similar o he one in Benigno and Benigno (006) wih sicky prices. 4
. Secion 3 derives he model used in his paper and displays is dynamic properies. Secion 4 solves he equilibrium under he Ramsey opimal moneary policy in boh cooperaive and noncooperaive regimes. Secion 5 derives he quadraic loss funcions around he Ramsey opimal seady saes obained in Secion 4. These are he welfare measures ha cenral banks aim o minimize. We also invesigae he naure of he opimal moneary policy in open economies wih nancial fricions. Secion 6 exends he basic model o cases wih inernaional lending and borrowing. Finally, Secion 7 summarizes he ndings of his paper and inroduces possible fuure exensions of his paper. Monopolisic Banking and Saggered Loan Conracs Nominal conracs ogeher wih infrequen renegoiaion are commonly observed in many counries. Thus, he sickiness of loan raes ogeher wih imperfec compeiion in he banking secor are poenially imporan mechanisms in accouning for he daa. Several previous sudies incorporae a similar banking secor in a dynamic general equilibrium framework. Gerali, Neri, Sessa, and Signorei (00), Mandelman (00, 0) and Fujiwara and Teranishi (0) develop models wih an imperfecly compeiive nancial secor. They all conclude ha an imperfecly compeiive banking secor conribues o a beer of he model o he daa. Gerali, Neri, Sessa, and Signorei (00) provide empirical evidence of he sickiness in loan conracs in his vein. They esimae he prooypical new Keynesian model, a la Smes and Wouers (003, 007) and Chrisiano, Eichenbaum, and Evans (005), and exend o replicae he aforemenioned feaures wih a monopolisic banking secor and loan rae sickiness. Shocks semming from he banking 5
secor explain he major par of he conracion in he recen nancial crisis. Mandelman (00, 0) nds ha he incorporaion of a monopolisic banking secor increases he volailiy of real variables and ampli es he business cycle. Counercyclical bank markups generaed from sraegic limi pricing aimed a proecing reail niches from poenial compeiors increases he model s o he daa in developing economies. Fujiwara and Teranishi (0) explain he persisence of he real exchange rae by incorporaing an imperfecly compeiive nancial secor. Also, Ravenna and Walsh (006) repor empirical evidence of a direc ineres rae e ec on in aion where marginal coss are a eced boh by real wages divided by he produciviy and nominal ineres raes. On implicaions of such nancial fricions on moneary policy, Ravenna and Walsh (006) inroduce he cos channel ino an oherwise sandard new Keynesian model in closed economy. The opimal moneary policy under he cos channel faces rade-o beween in aion and oupu gap sabilizaion even wih he IS shocks. Cooley and Quadrini (003) hin ha he decline in ineres raes afer he adven of Euro can be explained by moneary cooperaion in a wo-counry model wih he cos channel. No sudy, however, has invesigaed wheher nancial marke imperfecions call for policy cooperaion no only in he long-run bu also over business cycles. Such mechanisms can also replicae one of he imporan characerisics of moneary policy, ineres rae smoohing. Woodford (003) explains his hrough he hisory dependen policy under commimen. Graham and Wrigh (007), Kobayashi (008), and Teranishi (05) demonsrae ha rigidiies in loan rae dynamics can also necessiae ineres rae smoohing as he opimal policy reacion o shocks. 6 Fujiwara and Teranishi (0) also emphasize ha he sicky loan mechanism can produce hump-shaped 6 Conrary o Kobayashi (008), and Teranishi (05), sickiness in ineres raes is imposed on consumers in Graham and Wrigh (007). Thus, he loan ineres rae in he IS curve is sicky in Graham and Wrigh (007), while in our model, ha in he Phillips curve is sicky. Also, Graham and Wrigh (007) do no conduc welfare analysis bu show an ineresing resul on moneary policy. Low ineres raes are mainained even afer in aionary shocks hi he economy under sicky deb conracs. 6
responses o many srucural shocks including moneary policy shock. As previous lieraure on moneary policy ransmission mechanism using he Vecor Auoregressive models as represened by Chrisiano, Eichenbaum, and Evans (999) shows, he abiliy o produce hump-shaped responses is considered o be imporan for he dynamic sochasic general equilibrium model. As a resul, many sudies using he dynamic sochasic general equilibrium incorporae habi formaion in consumpion or invesmen growh adjusmen coss as examined in Chrisiano, Eichenbaum, and Evans (005). Sicky loan raes can have hump-shaped properies wihou relying on hese mechanisms. For a posiive analysis of nancial marke imperfecions, many sudies employ he - nancial acceleraor mechanism of Bernanke, Gerler, and Gilchris (999) in he dynamic sochasic general equilibrium framework. In he nancial acceleraor mechanism, ne worh as he sae variable causes he deviaions of loan raes from he policy ineres rae. In our model, insead of ne worh dynamics, he wedge beween he loan rae and he policy rae arises due o imperfec compeiion in rms and hus banks. Accordingly, he dynamics of loan raes are creaed by saggered loan conracs. The consequences are, however, similar. A shock relaed o nancial marke imperfecions evenually resuls in an increase in he cos of goods producion. 7 The bene of our approach is ha he naure of opimal moneary policy can be undersood analyically and herefore inuiively. 8 3 Model This secion describes a wo counry model wih nancial fricions. There are four agens in wo symmeric counries: consumers, rms, privae banks, and cenral banks. We rs display he problems solved by each agen and hen summarize equilibrium condiions. 7 This is also rue for he model wih collaeral consrains as in Kiyoaki and Moore (997). 8 For numerical analysis on opimal moneary policy in open economies wih such nancial fricions, see Bodensein, Guerrieri, and LaBriola (04). 7
The main model does no allow banks o lend and borrow inernaionally. Sill, nancial shocks spill over inernaionally, hrough expors and impors. Thus, nancial fricions in one counry can aler he dynamics of endogenous variables in he oher counry. The exension of he main model o inernaional lending and borrowing will be discussed in Secion 6. 3. Consumers A represenaive consumer in he home counry H maximizes welfare W : W E X T = T u (C T ) Z 0 v [l T (h)] dh ; () where E is he expecaions operaor condiional on he sae of naure a dae and [0; ) is he subjecive discoun facor. The funcions u and v are increasing in he consumpion index C and he labor supply l, respecively. l (h) denoes he labor supplied o inermediae-goods producing rm h. The budge consrain is given by P C + E [X ;+ B + ] + D B + ( + i ) D + + B + F T ; Z 0 w (h)l (h)dh () where P is he aggregae consumer price index, B is he Arrow securiy, D is he deposi o he privae banks, i is he nominal ineres rae se by he cenral bank from o, w is he nominal wage, B = R 0 B (h)dh is he nominal dividend from he ownership of he privae banks in he home counry, F = R 0 F (h)dh is he nominal dividend from he ownership of inermediae-goods producing rms in he home counry, X ;+ is he sochasic discoun facor, and T is he lump sum ax. 9 9 The resuls obained in his paper will no change even if a deposi o foreign banks or ownership of foreign rms and banks is allowed. 8
Because a complee nancial marke beween he wo counries is assumed, consumers in each counry can inernaionally rade he sae coningen securiies o insure agains counry-speci c shocks. Consequenly, consumers in boh counries encouner a unique discoun facor. Assuming a complee inernaional nancial marke in he presence of nancial marke imperfecions may seem unreasonable. These are, however, hough o be imporan ingrediens in explaining economic developmens during he recen global nancial crisis, in paricular, he signi can synchronizaion of he business cycles across di eren counries. Perri and Quadrini (0) explain his unprecedened degree of synchronizaion using a model wih credi shocks ( nancial marke imperfecions) under complee inernaional nancial markes. 3. Firms 3.. Inermediae-goods producer Inermediae-goods producer h produces a di ereniaed inermediae good y using he di ereniaed labor: y (h) + y (h) = f [l (h)] ; (3) and needs o borrow loans q o nance labor compensaion: q (h) = R (h) w (h) l (h); (4) where R is gross loan raes. The inermediae-goods producer h ses prices in boh domesic and foreign markes under he law of one price: 0 p (h) = S p (h) ; (5) 0 There is no need o assume eiher producer currency pricing or local currency pricing as here is no price sickiness. 9
o maximize he pro F : F (h) = ( + ) [p (h) y (h) + S p (h) y (h)] R (h) w (h) l (h); (6) where he aserisk denoes foreign variables. p and p denoe prices o home and foreign markes, respecively. S is nominal exchange raes. is he sales subsidy. Wih his ime-varying sales subsidy nanced by he lump-sum ax, he markup shock is de ned as exp ( ) ss markupime-variaion z } { z } { + ; where denoes he elasiciy of subsiuion beween di ereniaed inermediae goods. can capure ime-variaion in he markups. This is a speci caion following Benigno and Benigno (006) and creaes ine cien ucuaions in he marginal rae of subsiuion beween consumpion and goods producion. The same oucome is obained by using oher speci caions: ime-varying monopoly power of wage seers as in Clarida, Gali, and Gerler (00) and Woodford (003); a ime-varying elasiciy of subsiuion as in Giannoni (04). Under he curren seings, domesic (foreign) rms borrow only from domesic (foreign) banks. This assumpion will be relaxed laer in Secion 6 o check wheher inernaional lending and borrowing aler our main resuls. In his paper, sicky prices are no assumed o solely concenrae on he role of he nancial fricions on policy cooperaion. There is a rade-o beween price sabiliy and nancial sabiliy wih sicky prices. For deails of his rade-o, see Kobayashi (008) and Teranishi (05). 0
3.. Final-goods producer A nal consumpion goods producer minimizes he oal cos: P H; Y H; + P F; Y F; ; subjec o he following producion echnology: YH; YF; Y ; (7) where (0 ) denoes he home bias. is se o 0.5 since symmery beween wo counries is assumed. Goods produced in he domesic counry Y H; and hose produced in he foreign counry Y F; are de ned, respecively, as Z Y H; 0 y (h) dh ; (8) and Z Y F; 0 y (h ) dh : (9) 3.3 Privae Banks There is a coninuum of privae banks in each counry locaed over [0; ]. Each privae bank collecs deposis from consumers in is counry given saving ineres raes. Each bank h is in a long-erm relaionship wih each inermediae-goods producing rm h. This follows a segmened banking sysem assumed in such previous sudies as Kobayashi (008), Andrés and Arce (0) and Mandelman (00, 0). As a resul, i ses di ereniaed nominal loan ineres raes according o heir individual loan demand curves. A di ereniaed nominal loan ineres rae applies o di ereniaed inermediae-goods producers. Thus, wihin his segmened environmen, privae banks mainain monopoly
power over he loan ineres rae deerminaion. In addiion, each bank reses is loan ineres raes wih probabiliy following he Calvo (983) - Yun (996) framework as examined in Teranishi (05) and Fujiwara and Teranishi (0). Due o saggered loan conracs beween rms and privae banks, privae banks end up xing nominal loan ineres raes for a cerain period. Saggered loan conracs also generae dispersion in loan ineres raes, which resul in welfare coss, which will be explained in deail. The privae bank h ses he loan ineres rae o maximize he presen discouned value of pro : where X E T = T X ;T B T (h) ; (0) B (h) = q (h) [( + ) R (h) ( + i ) exp (u )] : () u denoes he loan premium shock. Noe ha goods prices are exible in his model. In addiion, he moneary auhoriy does no adjus nominal ineres raes on deposis i wih a Taylor rule arrangemen - a ypical feaure in he NOEM seup, alhough such an arrangemen is indeed possible. Nominal ineres raes on deposis are given by he opimal moneary policy discussed below. 3.3. Summary: Financial Markes In his economy, he benevolen cenral bank deermines nominal ineres raes i o maximize social welfare. Households ake i as deposi ineres raes and smooh consumpion hrough ineremporal opimizaion. Banks in he monopolisically compeiive marke borrow from households as deposis or loanable funds D wih deposi ineres raes i, Almos idenical resuls are obained wih he assumpion of he monopolisically compeiive banking secor as examined in Teranishi (05), Gerali, Neri, Sessa, and Signorei (00) and Fujiwara and Teranishi (0).
and lend o rm h wih lending raes R (h). A he beginning of he period, banks receive deposis and lend funds o rms. A he end of he period, hey receive repaymens from rms. If loan raes are exible, lending and borrowing are deermined by he inra-emporal opimizaion problem by privae banks, which is similar o he sandard saic pro maximizaion problem by rms. 3 When loan raes are sicky, rms solve he dynamic opimizaion problem o maximize he presen discouned value of he pro s as shown in equaions (0) and (). This is also analogous o he opimal price seing problem by rms under sicky prices in he sandard new Keynesian model. Wih he possibiliy ha rms may no be able change loan raes in he fuure, opimal loan rae seing becomes forward-looking. To focus on he role of nancial fricions, prices are assumed o be exible. I is herefore possible o assume ha he cenral bank can direcly conrol real (deposi) ineres raes. 4 The real ineres rae se by he cenral bank in his manner, however, is usually di eren from ha arising in he fricionless (e cien) economy, which can be called as he naural rae of ineres on deposis. The naural rae of ineres on deposis is deermined hrough he consumpion Euler equaion: C = E + i + C + = E ( + r + ) C +: r + becomes he naural rae of ineres on deposis when consumpion is always a is e cien (naural) level. 5 A wedge beween he curren deposi ineres rae and he naural rae of ineres on deposis may emerge afer (real) shocks hi he economy. 6 The cenral bank s role is 3 The di erence beween a monopolisic banking secor wih exible loan conracs and a perfecly compeiive banking secor is found only in he exisence of he seady sae markup in he former. No di erence arises in dynamics. 4 To be precise, as will be explained below, CPI in aion raes are lef o be indeerminae, bu CPI in aion expecaions are uniquely pinned down hrough he consumpion Euler equaion. 5 As is he case wih he sandard new Keynesian model, consumpion Euler equaions are no included in cenral banks welfare maximizaion problem since hey are redundan. 6 Shocks creae a wedge beween curren loan raes and hose under e cien economy. This will 3
how o minimize his wedge in order o maximize social welfare. Thus, reacions by he cenral bank o shocks aler deposi ineres raes, while loan ineres raes adjus only gradually due o saggered loan conracs. As will become clearer, compleely eliminaing he e ecs from shocks o loan raes is no necessarily he opimal moneary policy. Even if loan raes are exible, he cenral bank can improve social welfare in his model. Changes in he level of loan raes lead o ine cien ucuaions in oupu (and herefore consumpion evenually) under he working capial loan. Thus, exibiliy in loan raes does no preven he cenral bank from eliminaing ine cien ucuaions in oupu by adjusing nominal ineres raes o shocks. 3.4 Preference and Parameer u() and v() are iso-elasic funcions: u (c) = c ; and v (l) = l: Firms are equipped wih a linear producion echnology: f (l) = exp (z ) l; where z denoes he echnology shock. Appendix A displays he deailed derivaion for he sysem of equaions. evenually produce a wedge beween curren deposi raes and he naural rae of ineres on deposis. The naural rae of ineres is de ned so ha i corresponds o he policy ineres rae as is convenion in he sandard new Keynesian model. 4
3.5 Marke Clearing Condiions Equaion (3) ogeher wih he foreign counerpar depic he marke clearing condiions for inermediae goods. The marke clearing condiions for nal goods are simply C = Y ; () and C = Y : (3) Financial markes clear when oal deposis equal o oal loans: Z 0 q (h) dh = D ; and ne supply of he Arrow securiies is zero: B = 0: 3.5. Welfare Coss The saggered loan conrac creaes dispersion in loan ineres raes. Wih he working capial loan, loan raes are ighly linked wih labor supply. Dispersion in loan raes leads o ine cien allocaions of labor among ex pos symmeric rms like price dispersion in he sandard new Keynesian model. Similarly o Yun (005) for price dispersion, he relaive loan rae dispersion is de ned as Z R (h) dh; (4) 0 R 5
where R is he average loan raes: Z R R (h) 0 dh : (5) Then, aggregaing he resource consrains over h leads o P Y + P P H; Y PH;! = exp (z ) l : Any dispersion of loan raes, namely R (h) 6= R, works as if i were a negaive echnology shock. represens he welfare cos semming from saggered loan conracs. For he deails of he derivaion, see Appendix A, in paricular, equaion (85). 3.6 Sysem of Equaions equilibrium condiions below, ogeher wih he opimal moneary policy de ned in he nex secion deermine he opimal pahs for R, F, K, Y, R, F, K, l, l,,, i and i : 6 R 4 R 3 7 5 F = K ; (6) F = + E Y + R Y R + K = ( + i ) exp ( ) exp (u ) Y + + E R R 6 R 4 3 7 5 F +; (7) Y R R + K +; (8) F = K ; (9) Y + R = + E F Y R + F +; (0) 6
K = + i R Y + R + E Y 6 R = ( ) 4 Y R + K +; () exp ( ) R = l ; () R 3 7 5 + R R ; (3) Y R R 6 R = ( ) 4 = l ; (4) 3 7 5 R + R ; (5) and = Y exp ( ) R exp (z ) R : (6) Similarly o Yun (005), equaions (6) o (8) and equaions (9) o () represen he recursive represenaions for domesic and foreign loan Phillips curves, respecively. The rs-order log-linear approximaion on hese equaions around he Ramsey opimal seady saes (^x log (X =X) (X X) =X, where X is he Ramsey opimal seady sae value) leads o he domesic loan rae Phillips curve: ^R ^R = E ^R+ ^R + ( ) ( ) i + u + ^R ; (7) and he foreign loan rae Phillips curve: ^R ^R = E ^R + ^R + ( ) ( ) i ^R : (8) Equaions (7) and (8) are analogous o he new Keynesian Phillips curve. Insead of in aion raes, which are de ned as ^ = ^P ^P, here in aion raes for gross loan raes 7
( ^R ^R ) are deermined by loan in aion expecaion E ( ^R + ^R ) and (nominal) marginal coss of loan creaion (i + u + ^R ). Loan ineres raes a ec marginal coss wih he presence of he cos channel as equaions (4), (7) and (8) illusrae. Thus, conrary o he sandard new Keynesian model, in aion raes (of loan raes) as well as he price level (of loan raes) are pinned down by he model. Consequenly, backward-looking componens in equaions (7) and (8), namely ^R and ^R, become he endogenous sae variables in his model. Noe also ha seady saes do no maer for linearized aggregae supply condiions. Equaions (3) and (5) show he dynamics of relaive loan rae dispersion, which is de ned in equaion (4) and Z R (h ) dh : (9) 0 R Since each bank only reses is loan ineres raes wih probabiliy, equaions (3) and (5) are derived from he de niion of he average loan raes in equaion (5) and Z R 0 R (h ) dh : As is well-known in he lieraures wih he new Keynesian model, relaive price dispersion maers only under higher order han linear approximaion. This is because wih linear approximaion, ^ = ^ = 0: Equaions () and (4) are derived from he marke clearing condiions for inermediae goods in equaion (3) and is foreign counerpar. As is he case wih he sandard new Keynesian model, relaive price dispersion erms in equaions (4) and (9) ac as if hey were negaive echnology shocks. As a resul, price sabiliy, or loan rae sabiliy in his paper, becomes he opimal moneary policy. 8
Equaion (6) is he marke clearing condiion for he nal goods in equaions () and (3) under he complee inernaional nancial marke. This can be also expressed as log-deviaion from he Ramsey opimal seady saes as 0 = + ^Y + ^R z + ^R : (30) The consumpion Euler equaion for he domesic counry: Y Y + = ( + i ) E ; (3) + and ha for he foreign counry: " Y (Y ) = ( + i ) E + + # ; can be included in addiion o equilibrium condiions (6) o (6). These will deermine CPI in aion expecaions in boh counries. In such a model, however, indeerminacy in in aion raes arises. In order o avoid his indeerminacy, a sicky price mechanism mus be incorporaed in inermediae goods rms pro maximizaion problem in equaions (6). This will, however, complicae he analysis, especially in open economies. Thus, nominal price rigidiies are omied from he model and CPI in aion raes are lef o be indeerminae in his model. In his economy, here are hree disorions: subopimally low producion due o monopolisic rens, working capial loans, and saggered loan conracs. The rs disorion is eliminaed by an appropriae subsidy. The opimal moneary policy aims o minimize he welfare coss semming from he second and he hird disorions. 9
Figure : Responses o Moneary Policy Shock 3.7 Dynamic Properies Here, we display he dynamic propery of his model o he moneary policy shock. Even hough he model is quie simple and sylized, i can capure imporan properies in he moneary ransmission mechanism: namely, he delayed responses in loan raes and hump-shaped responses of oupu and consumpion. In he simples form, he linearized equilibrium condiions in equaions (7), (8) and (30) given policy ineres raes can deermine he equilibrium pahs for domesic loan raes R, foreign loan raes R and nal goods producion (consumpion in boh domesic and foreign counries) Y. The exisence of lagged loan raes in equaions (7) and (8) and he absence of he deerminaion of in aion raes give he model quie di eren implicaions regarding indeerminacy semming from moneary policy rules. The model can have unique raional expecaions equilibrium wihou moneary policy feedback rules. Figure illusraes he responses of hese variables o a moneary policy shock or an increase in policy ineres raes i, which is evenually deposi ineres raes in he consumpion Euler equaion in (3). The parameers are calibraed as in Table. and are aken from Seinsson (008), and is he average value of loan rae sickiness 0
Table : Parameer Values Parameers Values Explanaion 0.99 Subjecive discoun facor Coe cien of relaive risk aversionec o real ineres rae 0.57 Probabiliy of loan ineres rae change 7.66 Subsiuabiliy of di ereniaed consumpion goods across he counries esimaed in Fujiwara and Teranishi (0). The moneary policy shock follows an AR() process wih a parameer of 0.9. Due o he exisence of saggered loan conracs, he iniial response of domesic loan raes becomes signi canly smaller compared o changes in domesic policy ineres raes. Thus, delayed responses on loan raes repored by such previous sudies as Slovin and Sushka (983), Berger and Udell (99), Sorensen and Werner (006), Graham and Wrigh (007), Gambacora (008) and Gerali, Neri, Sessa, and Signorei (00) maerialize in his model. In addiion, he responses of Y, ha is he nal oupu and herefore consumpion in boh domesic and foreign counries, demonsrae humpshaped dynamics, ofen considered an imporan propery for he dynamic sochasic general equilibrium model o replicae. Hump-shaped responses sem from lagged loan raes in equaions (7) and (8) as endogenous sae variables. Unlike he sandard new Keynesian model wih sicky prices, he level of nominal variables price levels in he new Keynesian model and he levels of loan raes in our model consrain real variables hrough he working capial loan. The foreign loan rae Phillips curve in equaion (8) conains only foreign loan and policy ineres raes. A shock also only impacs upon domesic policy ineres raes. Thus, foreign loan raes remain a a seady sae level in his simulaion. Through an increase in domesic loan raes, however, consumpion in he foreign counry also decreases due o he cos channel of moneary policy under he complee inernaional nancial marke. We will consider opimal reacions by boh domesic and foreign cenral
banks in he following secions. 4 Ramsey Policy In his secion, he Ramsey opimal moneary policy under boh cooperaion and noncooperaion will be discussed. There are wo main aims of deriving he allocaions under he Ramsey opimal moneary policy in his secion: o compue he opimal Ramsey opimal seady sae around which he model should be approximaed, and o undersand wheher here are gains from cooperaion in he long-run. 4. Cooperaion Under cooperaion, wo cenral banks aim o maximize global welfare ogeher: W + W E " X T T = = E X T = C T + (C T ) Y T T l T l T ; Z 0 l T (h) dh Z 0 l T (h ) dh # (3) where equaions () and (3) are subsiued, subjec o equilibrium condiions in equaions (6) o (6). Appendix B provides all equilibrium condiions involving Lagrange mulipliers on he consrains of his problem. These deermine he allocaions under he opimal moneary policy in cooperaion. 4. Noncooperaion Under noncooperaion, he game beween wo cenral banks mus be well-de ned. In paricular, we mus clarify he acion of he opponen which is aken as given. In his paper, we solve he open-loop Nash equilibrium, where he domesic (foreign) cenral bank maximizes welfare of domesic (foreign) counry given he policy ineres rae in
he foreign (domesic) counry. Clarida, Gali, and Gerler (00) assume oupu in he oher counry o be given, while producer price in aion raes in he oher counry are considered o be given in Benigno and Benigno (003, 006). In he model considered in his paper, here is neiher counry speci c oupu nor in aion as can be seen in equaions (6) o (6). Consequenly, he naural variable o be given as exogenous o each cenral bank is he policy ineres rae in he counerpar counry. Given he policy ineres rae in he foreign counry i, he domesic cenral bank maximizes welfare in he domesic counry: W E X T = = E X T = C T T Y T T Z 0 l T ; l T (h) dh (33) subjec o equilibrium condiions in equaions (6) o (6). Similarly, he foreign cenral bank akes he policy ineres in he domesic counry i as given and maximizes welfare in he foreign counry: W E X T = Y T T l T ; (34) subjec o equilibrium condiions in equaions (6) o (6). Appendix B provides all equilibrium condiions involving Lagrange mulipliers on he consrains in his problem under noncooperaion. These deermine he allocaions under he opimal moneary policy in noncooperaion. 4.3 Ramsey Opimal Seady Sae The Ramsey opimal seady saes are compued from equilibrium condiions by eliminaing ime subscrips. The aim of compuing he Ramsey opimal seady saes is 3
wofold. Firs, we will derive he opimal moneary policy in he LQ framework following Benigno and Woodford (005) and Benigno and Benigno (006). This is because inuiion for he opimal moneary policy can hardly be undersood from he non-linear equilibrium condiions shown in Appendix B. LQ approximaion mus be conduced around he Ramsey opimal seady saes. Second, he di erences beween cooperaive and noncooperaive regimes imply he exisence of gains from policy cooperaion in he long-run. Appendix B shows he Ramsey opimal seady sae for all variables under boh cooperaion (wih subscrip C) and noncooperaion (wih subscrip N), where seady sae markups are eliminaed by subsidy. Here, only he Ramsey opimal seady saes of endogenous variables excep for auxiliary variables and he Lagrange mulipliers are displayed. The Ramsey opimal seady saes of policy ineres raes, oupu, labor supply and loan ineres raes under cooperaion are as follows: + i C = + i C = ; Y C = l C = l C = ; and R C = R C = : (35) Ne ineres raes are zero so he welfare coss semming from he working capial loan becomes zero. This is considered he Friedman rule in he presence of he cos channel. Zero ne nominal ineres raes ogeher wih negaive in aion raes become opimal in eliminaing nominal disorions. Thus, he second disorion can be eliminaed by he appropriae seady sae condiions wih negaive in aion argeing. 4
On he oher hand, hose under noncooperaion are + i N = + i N = + ; and Y N = l N = l N = ; + R N = R N = + : Since he coe cien of he relaive risk aversion, or, he inverse of he ineremporal elasiciy of subsiuion, is posiive ( > 0), boh policy and loan ineres raes are higher under he noncooperaive regime (i N > i C, R N > R C ). Regarding oupu and labor supply, since d + d = d exp log + d + = exp log + + log ( + ) > 0; (36) wheher or no i becomes larger under cooperaion depends on he size of. Appendix C proves ha seady sae welfare is indeed higher under cooperaion. 7 4.4 Cooperaion vs Noncooperaion in he Long-Run The Ramsey opimal seady saes under cooperaion are di eren from hose under noncooperaion. In addiion, seady sae welfare is naurally higher under cooperaion. Togeher hese imply ha here is welfare gain from cooperaion in he long-run. Here, we aim o undersand he sources of his long-run welfare gain. In he absence of shocks and nominal (loan rae) rigidiies, equilibrium condiions in 7 The model involves endogenous sae variables, namely R and R. Thus, seady sae welfare comparison may no be a good measure for evaluaing he (policy) regimes. In paricular, when he seady saes for endogenous sae variables are di eren, he seady saes under he Pareo opimal allocaion can be lower han hose under alernaive policy. For a deailed discussion on his poin, see Bilbiie, Fujiwara, and Ghironi (04). 5
equaions (6) o (6) collapse o he ve equaions below: Y f; + i f; = l f; ; (37) Y f; + i f; = l f;; (38) = Y f; ( + i f; ) + i f; ; (39) R f; = + i f; ; and R f; = + i f;; where he variables in his economy are denoed wih subscrip f. They can be also obained by eliminaing ime subscrips in equilibrium condiions in equaions (6) and (6). Thus, opimal policy analysis here can be considered o compue he golden rule allocaion in he erminology of King and Wolman (999). The problem under cooperaion is o maximize welfare de ned in (3) subjec o equaions (37) o (39), while he domesic (foreign) cenral bank under he noncooperaive regime aims o maximize welfare de ned in (33) and (34) subjec also o equaions (37) o (39). The opimal allocaions obained from hese problems are idenical o he Ramsey opimal seady saes, derived in he previous secion. The di erences in he Ramsey opimal seady saes beween cooperaion and noncooperaion can be undersood from his simpli ed opimizaion problem for he golden rule allocaions. Equaions (37) o (39) clarify he reason behind he di erences. Equaions (37) and (38) demonsrae ha each cenral bank has an incenive o keep policy ineres raes high o reduce he dis-uiliy semming from labor supply. Corsei and Peseni (00) call his incenive he de aionary bias. Wih he working capial loan and he complee nancial marke, he erms of rade T ot can be expressed as he raio of domesic over 6
foreign loan raes: 8 T ot = S P H; P F; = R : (40) R Thus, each cenral bank aims o keep higher ineres raes o improve he erms of rade. On he oher hand, equaion (39), which is derived from he marke clearing condiion for nal goods in equaions () and (3) under he complee inernaional nancial marke, shows ha wih globally lowered ineres raes, boh counries can enjoy more consumpion and herefore higher welfare. Under he complee inernaional nancial marke, i is no he policy ineres rae in each individual counry, bu global ineres raes, ha is he arihmeic mean of ineres raes of wo counries, which deermines global consumpion and herefore consumpion in each counry. This becomes he source of he exernaliy, which creaes incenives for cenral banks o keep ineres raes higher. Cenral banks under cooperaion can inernalize his exernaliy. Consequenly, ineres raes under cooperaion are lower han under noncooperaion. Thus, here are gains in cooperaion wih he cos channel in he long-run. 9 5 Opimal Moneary Policy in LQ Framework The previous secion clari es ha here are gains in cooperaion in he long-run. In his secion, we delve ino wheher gains exis even in he shor-run, in paricular, in opimal responses o srucural shocks. For his, we need o compare he opimal pahs o shocks of all endogenous variables beween cooperaion and noncooperaion using equilibrium condiions in Appendix B. 0 Ye, here are oo many equaions, in paricular, for auxiliary variables and co-sae variables. Insead, in his secion, we invesigae he naure of he Ramsey opimal 8 For he deailed derivaion, see Appendix A, in paricular, equaions (89) o (9). 9 Cooley and Quadrini (003) explain he decline in ineres raes afer he adven of Euro were caused by moneary cooperaion. 0 Naurally, he same impulse responses are obained under boh non-linear and LQ Ramsey problems. 7
policy using he LQ framework proposed by Benigno and Woodford (005) and Benigno and Benigno (006). 5. Loss Funcion under Cooperaion Firs, welfare under cooperaion in (3) is approximaed up o he second order. We use he second order log approximaion: X X X ^x + ^x : Then, welfare under cooperaion in (3) is approximaed around he Ramsey opimal seady sae as W + W E X T = E X =0 Y T T l T l T ^Y ^l ^l + ( ) ^Y ^l ^l : (4) Noe ha erms ha are of he higher order han second order and independen from policy will no be shown hereafer. By aking logs for equaions () and (4), we have ( ) ^Y ^R + ^ = ^l ; (4) and ( ) ^Y ^R + ^ = ^l : (43) Benigno and Benigno (006) is he applicaion of Benigno and Woodford (005) o a wo counry model. De Paoli (009) derives he quadraic loss funcion in a small open economy using his echnique. 8
In addiion, second order approximaion o equaions (3) and (5) leads o E X =0 E X =0 ^R ^R ; (44) ( ) ( ) and E X =0 E X =0 ( ) ( ) ^R ^R : (45) By subsiuing equaions (4) o (45) ino (4), he quadraic loss funcion under cooperaion is derived: (W + W ) L E X =0 8 >< >: ^R ^R ( )( ) + ( )( ) + ^R + + ^R h ^R + + ^R + i ^R ^R 9 >= : >; (46) The loss funcion in equaion (46) shows ha global welfare is represened by no only he loan in aion rae, namely he di erence ( ^R ^R ), bu also he level of loan ineres raes ^R. The former capures welfare coss semming from relaive loan rae dispersion in equaions (4) and (9). The laer represens welfare losses from unsmoohed consumpion. The cos channel conrols he equilibrium dynamics in consumpion and herefore, loan raes remain in he approximaed loss funcion o represen welfare gain from consumpion smoohing. 5. Loss Funcions under Noncooperaion Under noncooperaion, he loss funcions for boh domesic and foreign cenral banks are compued separaely. The domesic welfare under noncooperaion in (33) is approx- 9
imaed up o he second order as W E X T = + Y T T E X =0 l T ( + ) ^Y ( + ) ( ) ^l + ^Y ^l : (47) Afer subsiuing equaions (4) o (44) and ignoring he parameers before he summaion, his collapses o E X =0 8 >< >: 4 ^R ^R ( )( ) ^R + ^R + ^R z + ^R + + 9 >= >; : (48) Conrary o he loss funcion under cooperaion in (46), he linear erm ^R sill remains. ^R represens he erms of rade exernaliy. The domesic cenral bank prefers ^R o be lower since his reduces social loss in (48). This is because lower ^R improves he erms of rade for he domesic counry as shown in equaion (40). A linear erm in he welfare meric will resul in a spurious welfare evaluaion in he LQ framework. Here, following Benigno and Woodford (005) and Benigno and Benigno (006), we ake he second order approximaion o equilibrium condiions and obain he approximaed equaions where linear erms are expressed only by quadraic erms. By using such second orderly approximaed equilibrium condiions, we can subsiue ou linear erms in he welfare meric wih quadraic erms. Appendix D shows furher deail of how o derive he quadraic approximaion of he loan rae Phillips curves in equaions (6) o (8) or (9) o (). From he second order approximaion of he loan rae Phillips curve in he foreign counry in equaions (9) o For deails on his, see, for example, Suherland (00), Kim and Kim (003, 007), Benigno and Woodford (005, 0) and Kim, Kim, Schaumburg, and Sims (008). 30
(), we can derive E X =0 i ^R E X =0 6 4 ( ) ^Y i ( )( ) ^R ^R i ^R ^R 3 7 5 : (49) By subsiuing his approximaed relaionship in (49) ino he approximaed welfare measure in (48), we can derive he quadraic loss funcion which he domesic cenral bank aims o minimize: L D E X =0 8 >< >: ^R ^R ( )( ) + + ( )( ) i + ^R + + ^R h ^R + + ^R i ^R i ^R 9 >= : (50) >; Similarly, from he second order approximaion of he loan rae Phillips curve in he domesic counry in equaions (6) o (8), we can obain 8 hz + ( ) ^Y i i + + u ^R 9 E X =0 i ^R + u + E X =0 >< >: i + u + ^R ^R ^R ( )( ) >= : >; (5) By using his approximaed relaionship in (5), we can derive he quadraic loss funcion for he foreign cenral bank as L F E X =0 8 >< >: ^R ^R ( )( ) + ^R ( )( ) h + ^R (i + + u )i + ^R nh ^R (i + + u )i + ^R + o ^R 9 >= : (5) >; 3
5.3 Cooperaion vs Noncooperaion in he Shor-Run We rs de ne he opimal allocaions in he LQ framework as follows. 3 De niion The opimal cooperaive allocaion is he sequence of endogenous variables f ^R ; ^R ; i ; i ; ^Y g ha minimizes (46) under he consrains (7), (8), and (30), given he sequence of shocks fu ; z ; g and he iniial condiions: ^R0 and ^R 0. De niion The opimal noncooperaive allocaion is he sequence of endogenous variables f ^R ; ^R ; i ; i ; ^Y g, ha minimizes (50) under he consrains (7), (8), and (30), given he sequence of he foreign policy ineres rae i, shocks fu ; ; z g and he iniial condiions: ^R0 and ^R 0, and ha minimizes (5) under he consrains (7), (8), and (30), given he sequence of he domesic policy ineres rae i, shocks fu ; z ; g and he iniial condiions: ^R0 and ^R 0. Noe ha parameers in equaions (7), (8) and (30) do no rely on seady sae values. Also, regarding he loss funcions in (46), (50) and (5), he di erence in seady saes only maers for he parameers before he summaion as in (47), which can be ignored when compuing he opimal moneary policy. Therefore, even hough he Ramsey seady saes are di eren beween cooperaion and noncooperaion, opimal responses are no a eced by his di erence. Below, we describe how he opimal moneary policy under boh cooperaion and noncooperaion will reac o he echnology shock, he loan premium shock and he markup shock, respecively. 5.3. Technology Shock Noe ha he echnology shock z is no included in he loss funcions under boh cooperaion and noncooperaion, as shown in equaions (46), (50) and (5). This fac implies 3 ^Y is passively deermined via equaion (30). Thus, i can be excluded from he deerminaion of opimal moneary policy. 3
ha he level of loan raes or loan in aion raes, ha he cenral banks aim o achieve, are independen from he echnology shock. In a sandard new Keynesian model, due o sicky prices, he echnology shock alers he naural rae, namely oupu under he exible price equilibrium. Therefore, he oupu gap, which is de ned as he di erence in oupu beween he sicky and exible price equilibria and hus he cenral banks aim o minimize, also shifs as he echnology shock changes. In conras, in our model, due o he exibiliy in price seings, he echnology shock does no change he oupu gap. Thus, for he cenral bank, i is opimal o sabilize ucuaions in loan raes deermined by equaions (7) and (8). These equaions do no conain he echnology shock as a componen of marginal coss for supplying loans. Under boh cooperaion and noncooperaion, i is opimal o compleely sabilize he ucuaions in loan raes in boh domesic and foreign counries. Any ucuaions in oupu ^Y according o equaion (30) under ^R = ^R = 0, namely, ^Y = z are opimal and should no be correced by policy acions. Thus, here is no addiional gain from cooperaion. 5.3. Loan Premium Shock Conrary o he echnology shock, he loan premium shock is included in he loss funcion in he foreign counry as in equaion (5) as well as in he domesic loan rae Phillips curve in equaion (7). Despie his, he loan premium shock does no require policy cooperaion eiher. Under cooperaion, since he loan premium shock is no included in he global loss funcion in equaion (46), cenral banks in boh counries should aim o achieve complee 33
loan rae sabiliy as ^R = ^R = 0. This can be achieved by seing he domesic policy ineres rae o eliminae he domesic loan premium shock in he domesic loan Phillips curve in equaion (7) such ha i = u. Under noncooperaion, he domesic cenral bank aims o compleely sabilize loan raes since he loss funcion does no conain he loan premium shock. To achieve his, again, he domesic policy rae is se o eliminae he loan premium shock. By doing so, loan raes are compleely sabilized, since he marginal coss of supplying domesic loans in equaion (7) are no ucuaing. Alhough he loan premium shock is included in he foreign loss funcion in equaion (5), he domesic policy ineres rae is no conrollable by he foreign cenral bank. Consequenly, he complee sabilizaion of loan raes by he domesic cenral bank su ces o achieve he opimal allocaions. Again, here is no gain from cooperaion. 5.3.3 Markup Shock The markup shock is repored o be an imporan driver of he business cycles in many sudies wih he prooypical DSGE model following Chrisiano, Eichenbaum, and Evans (005) and Smes and Wouers (003, 007). Bayesian maximum likelihood esimaion of he DSGE model of he Euro area by Gerali, Neri, Sessa, and Signorei (00) provides sizable esimaes of sandard errors in he banking secor markup shocks. Also, he auhors repor signi can conribuions from markup shocks in he banking secor in he ucuaions of nancial (and herefore real economic) variables beween 004 and 009 including he peak of he recen global nancial crisis. The opimal responses o he markup shock under boh cooperaion and noncooperaion are shown in Figures and 3. The markup shock follows an AR() process wih a parameer of 0.9. Responses o shocks are derived under commimen ogeher wih he assumpion ha he iniial endogenous sae variables are se a heir opimal seady 34